Set Theory Commons^™

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră ...

An Introduction To Set Theory And Topology, Ronald C. Freiwald

Books and Monographs

These notes are an introduction to set theory and topology. They are the result of teaching a two-semester course sequence on these topics for many years at Washington University in St. Louis. Typically the students were advanced undergraduate mathematics majors, a few beginning graduate students in mathematics, and some graduate students from other areas that included economics and engineering. The usual background for the material is an introductory undergraduate analysis course, mostly because it provides a solid introduction to Euclidean space Rn and practice with rigorous arguments — in particular, about continuity. Strictly speaking, however, the material is mostly self-contained. Examples ...

Elementary Set Theory, Richard P. Millspaugh

Open Educational Resources

This text is appropriate for a course that introduces undergraduates to proofs. The material includes elementary symbolic logic, logical arguments, basic set theory, functions and relations, the real number system, and an introduction to cardinality. The text is intended to be readable for sophomore and better freshmen majoring in mathematics.

The source files for the text can be found at https://github.com/RPMillspaugh/SetTheory

Axioms Of Set Theory And Equivalents Of Axiom Of Choice, Farighon Abdul Rahim

Mathematics Undergraduate Theses

Sets are all around us. A bag of potato chips, for instance, is a set containing certain number of individual chip's that are its elements. University is another example of a set with students as its elements. By elements, we mean members. But sets should not be confused as to what they really are. A daughter of a blacksmith is an element of a set that contains her mother, father, and her siblings. Then this set is an element of a set that contains all the other families that live in the nearby town. So a set itself can ...

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Introduction To Game Theory: A Discovery Approach, Jennifer Firkins Nordstrom

Linfield Authors Book Gallery

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in ...

Optimizing Networking Topologies With Shortest Path Algorithms, Jordan Sahs

Student Research and Creative Activity Fair

Communication networks tend to contain redundant devices and mediums of transmission, thus the need to locate, document, and optimize networks is increasingly becoming necessary. However, many people do not know where to start the optimization progress. What is network topology? What is this “Shortest Path Problem”, and how can it be used to better my network? These questions are presented, taught, and answered within this paper. To supplement the reader’s understanding there are thirty-eight figures in the paper that are used to help convey and compartmentalize the learning process needed to grasp the materials presented in the ending sections ...

Transfinite Ordinal Arithmetic, James Roger Clark

All Student Theses

Following the literature from the origin of Set Theory in the late 19th century to more current times, an arithmetic of finite and transfinite ordinal numbers is outlined. The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. With the fundamental notion of counting addressed: then addition, multiplication, and exponentiation are defined and developed by established fundamentals of Set Theory. Many known theorems are based upon this foundation. Ultimately, as part of the conclusion ...

The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates

Undergraduate Theses and Capstone Projects

We study graph colorings of the form made popular by the four-color theorem. Proved by Appel and Haken in 1976, the Four-Color Theorem states that all planar graphs can be vertex-colored with at most four colors. We consider an alternate way to prove the Four-Color Theorem, introduced by Hadwiger in 1943 and commonly know as Hadwiger’s Conjecture. In addition, we examine the chromatic number of graphs which are not planar. More specifically, we explore adding edges to a planar graph to create a non-planar graph which has the same chromatic number as the planar graph which we started from.

Computable Reducibility Of Equivalence Relations, Marcello Gianni Krakoff

Boise State University Theses and Dissertations

Computable reducibility of equivalence relations is a tool to compare the complexity of equivalence relations on natural numbers. Its use is important to those doing Borel equivalence relation theory, computability theory, and computable structure theory. In this thesis, we compare many naturally occurring equivalence relations with respect to computable reducibility. We will then define a jump operator on equivalence relations and study proprieties of this operation and its iteration. We will then apply this new jump operation by studying its effect on the isomorphism relations of well-founded computable trees.